If you don't have any house members left, you cannot conquer any new neutral solar systems. In this case, you have to attack enemy imperators, in order to expand your empire. (Of course, you can only attack solar systems, which do not belong to your house - their map color must differ from red or yellow!).

The word in case is the last. I think it is clear that it is not that intelligent to try to conquer your own systems. In my opinion this word should change to orange, so that erveryone know that orange is the colour of the subordinates.